Problem: Solve for $x$ and $y$ using elimination. ${-4x-2y = -16}$ ${-5x-2y = -18}$
Answer: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the bottom equation by $-1$ ${-4x-2y = -16}$ $5x+2y = 18$ Add the top and bottom equations together. ${x = 2}$ Now that you know ${x = 2}$ , plug it back into $\thinspace {-4x-2y = -16}\thinspace$ to find $y$ ${-4}{(2)}{ - 2y = -16}$ $-8-2y = -16$ $-8{+8} - 2y = -16{+8}$ $-2y = -8$ $\dfrac{-2y}{{-2}} = \dfrac{-8}{{-2}}$ ${y = 4}$ You can also plug ${x = 2}$ into $\thinspace {-5x-2y = -18}\thinspace$ and get the same answer for $y$ : ${-5}{(2)}{ - 2y = -18}$ ${y = 4}$